# Square Root of 105 | Top Q&A

Square Root of 105 The square root of 105 is the inverse of the square of a number (a) such that a × a = 105. The number 105 has both positive and negative square roots. The square root can be a real number or an imaginary number. We will now find the value of the square root of 105 using the long division method and the approximation method.

• Square root of 105: 105 = 10.24695
• Square 105: (105) 2 = 11025

1. What is the square root of 105? 2. Is the square root of 105 Reasonable or Unreasonable? 3. How to Find the Square Root of 105? 4. Important Notes about the Square Root of 105 5. Frequently Asked Questions about the Square Root of 105

• The square root of 105 in decimal is 10.2469
• The square root of 105 is expressed as √105 in root form.
• The square root of 105 is expressed as (105) 1/2 in exponential form.
• The square root of 105 is a non-terminating and non-repeating number.
• Therefore, it cannot be expressed as p/q where q ≠ 0.
• Therefore, the square root of 105 is an irrational number.

### Square root of 105 using approximation

• Find two consecutive perfect squares of which 105 lie. In this case, the numbers are 10 (100) and 11 (121). So the integer part of the square root of 105 is 10
• Now for the decimal part we will use the below formula: (Given number – Smaller perfect square) / (Larger perfect square – Smaller perfect square) = (105 – 100) / (121 – 100) = 5/21 = 0.238
• Therefore, approx. the value of the square root of 105 by approximation is 10.238

### Square root of 105 equals Long Division

Now we will calculate the square root of 105 using the long division method.

• Start matching the numbers by placing a stick on top of them from the right side of the number 105 in pairs of two. Here we will have two pairs 05 and 1 (matched from right to).
• Now, find a number (n) whose square is ≤ 1. The value of n will be 1 because 1 × 1 = 1≤ 1.
• We get the quotient (1). Now, by adding the divisor n to itself and get the new divisor 2n(2).
• Drag the next pair down (the new dividend becomes 005) and find a number (A) such that 2A × A ≤ 5. In this case, the value of A will be 0.
• Now put a decimal at the same time after 5 in the dividend and after 1 in the quotient. Alternatively, put 3 pairs of zeros in the dividend after the decimal (105. 00 00 00) and repeat the above step for the remaining three pairs of zeros.

So we get the value of the square root of √105 = 10,246 using the long division method.Explore square roots using interactive illustrations and examples

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• The square root of 105 is an irrational number.
• The number 105 is not a perfect square.
• The square root of -105 is an imaginary number.

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